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Transmission coefficient of a 1/r potential

The potential is v = V0r0/r for r>r0 or v= <<<0 for r<r0.
Considering a particle of 0<E<<V0 initially in 0<r<r0, show that the transmission coefficient can be approximated by T ~ -(2/hbar) int from r0 to r1 of sqrt( 2mV(r)-E dr. r1 is the value of r for which E=V(r1).

I'm not really sure how to go about approaching this question. Our tutor said to approximate the 1/r potential as a series of finite square barriers, and to consider the transmission through each barrier. However in my notes it says that if gamma*a is very small (2a is the width of the barrier) then T goes to 1 which doesn't really help me :confused:

I'd just appreciate some tips on where to start, I don't want the full solution. Thanks
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MC REN
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suneilr
The potential is v = V0r0/r for r>r0 or v= <<<0 for r<r0.
Considering a particle of 0<E<<V0 initially in 0<r<r0, show that the transmission coefficient can be approximated by T ~ -(2/hbar) int from r0 to r1 of sqrt( 2mV(r)-E dr. r1 is the value of r for which E=V(r1).

I'm not really sure how to go about approaching this question. Our tutor said to approximate the 1/r potential as a series of finite square barriers, and to consider the transmission through each barrier. However in my notes it says that if gamma*a is very small (2a is the width of the barrier) then T goes to 1 which doesn't really help me :confused:

I'd just appreciate some tips on where to start, I don't want the full solution. Thanks


Presumably you have/can derive a solution for the transmission through a barrier of width a?

If so, then use this, but don't take the limit a -> 0 (where T->1), but sum these (and let a -> dr I guess for the integral)

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